Exam-Style Questions.

1.	GCSE Higher

Without using a calculator, show clearly that \(27^{\frac23}\) is equal to \(9\).

Worked Solution

---

2.	GCSE Higher

There's an old Elvish wives tale that roughly translated reads:

Four To The Half Power Is Simple To Do

Just Halve The Four And The Answer Is Two.

Modern-day Elves extend this method to calculate other powers such as

$$ 16^{ \frac{1}{4}} = \frac{1}{4} \text{ of } 16 = 4 $$

Is this calculation correct? If it is not explain what is wrong.

Worked Solution

---

3.	GCSE Higher

$$ 9^{\frac{1}{3}} \times 3^n = 27^{\frac{4}{5}} $$

Work out the exact value of \(n\).

Worked Solution

---

4.	GCSE Higher

Without using a calculator find the values of the following:

(a) \(25^{-\frac12} \)

(b) \( \left( \frac{27}{64} \right)^{ \frac23} \)

Worked Solution

---

5.	GCSE Higher

If a, b and c are positive integers use the following statements to find the values of a, b and c.

$$ (ab^c)^3 = 27b^{21} $$ $$ b= 9a $$

Worked Solution

---

6.	GCSE Higher

\(y = a \times b^{x – 2}\) where \(a\) and \(b\) are numbers.

\(y = 5\) when \(x = 2\)

\(y = 0.005\) when \(x = 5\)

Work out the value of \(y\) when \(x = 4\)

Worked Solution

---